Contents

  1. Imports

  2. Defining the Data Directory and Result Directory

  3. Extracting Center Information

    1. Initializing the Classes
    2. Determining the Region of Interest
    3. Reiniatilizing the Classes
    4. Setting the Reference Image
    5. Extracting Center Related Information
    6. Some Preliminary Analysis
      1. None Values
      2. Sample Images
  4. Extracting Informations From DataFrame
    1. Frame Informations
      1. Information About DataFrame
      2. Information about Frames Numbers
        1. Getting Numerical Frame Number
      3. Creating New Columns
        1. The Region and Time
        2. The Speeds
        3. Angle
      4. Extracting Values
        1. Height
        2. Angles
        3. Speeds
  5. Fitting Curves
    1. The Curves to be Fitted
    2. Region III
      1. Data For Region III
      2. Fitting the Curves In Region III
      3. Caparing Results For Region III
      4. Calculating Informations From Parameters In Region III
        1. The Speeds In Region III
        2. The Angle In Region III
      5. Visualizating Results In Region III
        1. x and y Coordinates In Region III
        2. Speeds In Region III
        3. Angle In Region III
      6. Getting The Required Informations In Region III
      7. Adding the Information for Region III to DataFrame
    3. Region I
      1. Data For Region I
      2. Fitting the Curves
      3. Caparing Results
      4. Calculating Informations From Parameters
        1. The Speeds
        2. The Angle
      5. Visualizating Results
        1. x and y Coordinates
        2. Speeds
        3. Angle
      6. Getting The Required Informations
  6. Adding the Additional Information
    1. Saving Informations to DataFrame
    2. The Text Information
      1. Creating the Text
      2. Save the DataFrames

Imports¶

In [ ]:
from extract_center import CenterExtracter
from run import Run
from misc_tools import Plotter, Smoother
from functools import partial
import re
import numpy as np
import matplotlib
import matplotlib.pyplot as plt
import pandas as pd
from scipy.optimize import curve_fit
import warnings

warnings.filterwarnings("ignore")
plt.rcdefaults()
matplotlib.rcParams["figure.figsize"] = (8, 6)

Defining the Data Directory and Result Directory¶

In [ ]:
sequence = "ref"
DATA_DIR = "../../data/extracted_images/" + sequence
RESULT_DIR = "../../data/results/" + sequence

Extracting Center Information¶

Initializing the Classes¶

In [ ]:
run = Run(DATA_DIR, RESULT_DIR)
ce = CenterExtracter()

Determining the Region of Interest¶

In [ ]:
images = run.get_images()
img_1 = ce._read_image(images[0])
ce._show_image(img_1)
In [ ]:
region_of_interset = (850, 350, 950, 450)

Reiniatilizing the Classes¶

In [ ]:
run = Run(DATA_DIR, RESULT_DIR, region=region_of_interset)

Setting the Reference Image¶

In [ ]:
run._set_ref_image(-10)

Extracting Center Related Information¶

In [ ]:
df = run.all_points(
    crop_included=True, binary=True, verbose=False, num_images=None, raise_error=False, file_name="dynamic_ap.csv",
)

Getting list of images...
Extracting data from images...

Extracting data from images: 100%|██████████| 171/171 [00:06<00:00, 25.70it/s]
Saving to csv...
Done!




























Some Preliminary Analysis¶






















None Values¶


















In [ ]:



     


df.isna().sum()



     






















    
    
Out[ ]:








id       0
x        3
y        3
r1       3
r2       3
theta    3
dtype: int64
























In [ ]:



     


none_values = df.isna().sum()["x"]
total_frames = len(df)
unrealistic = len(
    df[((df["r1"] + df["r2"]) / 2 > 20) | ((df["r1"] + df["r2"]) / 2 < 5)]
)



     



















In [ ]:



     


none_values, unrealistic



     






















    
    
Out[ ]:








(3, 3)
























In [ ]:



     


df = pd.read_csv(RESULT_DIR + "/dynamic_ap.csv")



     























Sample Images¶


















In [ ]:



     


p = Plotter(df, RESULT_DIR)
p.get_samples(25, file_name=f"{sequence}_samples.png")



     






















    
    



































Extracting Informations From DataFrame¶






















Frame Informations¶






















Information About DataFrame¶


















In [ ]:



     


df = pd.read_csv(RESULT_DIR + "/dynamic_ap.csv")



     



















In [ ]:



     


none_frames = df.isna().sum()["x"]
total_frames = len(df)
unrealistic = len(
    df[((df["r1"] + df["r2"]) / 2 > 20) | ((df["r1"] + df["r2"]) / 2 < 5)]
)



     























Information about Frames Numbers¶


















In [ ]:



     


info_dict = {
    "first_frame": 1,
    "last_frame": 2,
    "contact_frame": 3,
    "leave_frame": 4,
    "angle": 5,
    "passthrough": 6,
}



     



















In [ ]:



     


def get_info(file):
    information = {}
    with open(file, "r") as f:
        texts = f.readlines()
    for key, value in info_dict.items():
        line = texts[value]
        info = line.split(":")[1].strip()
        information[key] = info
    return information


information = get_info(f"{DATA_DIR}.txt")



     



















In [ ]:



     


first_frame = DATA_DIR + "/" + information["first_frame"]
last_frame = DATA_DIR + "/" + information["last_frame"]
contact_frame = DATA_DIR + "/" + information["contact_frame"]
angle = information["angle"]
leave_frame = DATA_DIR + "/" + information["leave_frame"]
passthrough = information["passthrough"]



     























Getting Numerical Frame Number¶


















In [ ]:



     


reg = re.compile(r"\d{3}")
first_frame_num = int(reg.findall(first_frame)[0])
contact_frame_num = int(reg.findall(contact_frame)[0])
leave_frame_num = int(reg.findall(leave_frame)[0])
last_frame_num = int(reg.findall(last_frame)[0])
first_frame_num, contact_frame_num, leave_frame_num, last_frame_num



     






















    
    
Out[ ]:








(17, 68, 107, 161)
























In [ ]:



     


df = df.loc[:last_frame_num]



     























Creating New Columns¶






















The Region and Time¶


















In [ ]:



     


s = Smoother(df)
df_s = s.smoothen(remove_noise=False)
df_c = df[df["x"].notna()]



     



















In [ ]:



     


def get_region(id):
    id = id.split("/")[-1].split(".")[0]
    id = int(id)
    if id<=first_frame_num:
        return "O"
    elif id>=first_frame_num and id<=contact_frame_num:
        return "I"
    elif id>=contact_frame_num and id<=leave_frame_num:
        return "II"
    else:
        return "III"



     



















In [ ]:



     


df_c["Region"] = df_c["id"].apply(get_region)
df_s["Region"] = df_s["id"].apply(get_region)



     



















In [ ]:



     


def get_time(id):
    id = id.split("/")[-1].split(".")[0]
    id = int(id)
    return id



     



















In [ ]:



     


df_c["time"] = df_c["id"].apply(get_time)
df_s["time"] = df_s["id"].apply(get_time)



     























The Speeds¶


















In [ ]:



     


df_s["vx"] = df_s["x"].diff(7) / 7
df_s["vy"] = df_s["y"].diff(7) / 7
df_s.dropna(inplace=True)
df_s["vx"] = df_s["vx"].astype(float)
df_s["vy"] = df_s["vy"].astype(float)
df_s["v"] = np.sqrt(df_s["vx"] ** 2 + df_s["vy"] ** 2)

df_c["vx"] = df_c["x"].diff(7) / 7
df_c["vy"] = df_c["y"].diff(7) / 7
df_c.dropna(inplace=True)
df_c["vx"] = df_c["vx"].astype(float)
df_c["vy"] = df_c["vy"].astype(float)
df_c["v"] = np.sqrt(df_c["vx"] ** 2 + df_c["vy"] ** 2)



     



















In [ ]:



     


# plt.plot(df_s["vy"], label = "smoothened")
# plt.plot(df_c["vy"], label = "raw")
# plt.legend();



     



















In [ ]:



     


# plt.plot(df_s["v"], label = "smoothened")
# plt.plot(df_c["v"], label = "raw")
# plt.legend();



     























Angle¶


















In [ ]:



     


def get_angle(row):
    vx = row["vx"]
    vy = -row["vy"]
    if vx == 0 and vy == 0:
        return 0
    elif vx == 0:
        return 90
    else:
        return np.arctan(vy / vx) * 180 / np.pi



     



















In [ ]:



     


df_s["angle"] = df_s.apply(get_angle, axis=1)
df_c["angle"] = df_c.apply(get_angle, axis=1)



     



















In [ ]:



     


# plt.plot(df_s["angle"], label = "smoothened")
# plt.plot(df_c["angle"], label = "raw")
# plt.legend();



     























Extracting Values¶






















Height¶


















In [ ]:



     


y0 = df_c[df_c["time"] == first_frame_num]["y"].values[0]
yc = df_c[df_c["time"] == contact_frame_num]["y"].values[0]
hc = yc - y0

y0 = df_s[df_s["time"] == first_frame_num]["y"].values[0]
ys = df_s[df_s["time"] == contact_frame_num]["y"].values[0]
hs = ys - y0
hc, hs



     






















    
    
Out[ ]:








(161.0, 164.28606541879378)




























Angles¶


















In [ ]:



     


df_c[df_c["time"] == contact_frame_num].T



     






















    
    
Out[ ]:











  
    

      
      68
    

  
  
    

      id
      ../../data/extracted_images/ref/068.jpg
    

    

      x
      866.0
    

    

      y
      571.0
    

    

      r1
      10.0
    

    

      r2
      9.0
    

    

      theta
      17.188734
    

    

      Region
      I
    

    

      time
      68
    

    

      vx
      -0.142857
    

    

      vy
      4.857143
    

    

      v
      4.859243
    

    

      angle
      88.315316
    

  



























In [ ]:



     


df_c[df_c["time"] == leave_frame_num].T



     






















    
    
Out[ ]:











  
    

      
      107
    

  
  
    

      id
      ../../data/extracted_images/ref/107.jpg
    

    

      x
      965.0
    

    

      y
      610.0
    

    

      r1
      11.0
    

    

      r2
      9.0
    

    

      theta
      43.544792
    

    

      Region
      II
    

    

      time
      107
    

    

      vx
      5.428571
    

    

      vy
      -3.142857
    

    

      v
      6.272714
    

    

      angle
      30.068583
    

  



























In [ ]:



     


df_s[df_s["time"] == contact_frame_num].T



     






















    
    
Out[ ]:











  
    

      
      68
    

  
  
    

      id
      ../../data/extracted_images/ref/068.jpg
    

    

      x
      865.451125
    

    

      y
      574.445453
    

    

      r1
      9.818302
    

    

      r2
      9.164681
    

    

      theta
      66.866092
    

    

      r
      9.220079
    

    

      Region
      I
    

    

      time
      68
    

    

      vx
      -0.064635
    

    

      vy
      5.278286
    

    

      v
      5.278682
    

    

      angle
      89.298417
    

  



























In [ ]:



     


df_s[df_s["time"] == leave_frame_num].T



     






















    
    
Out[ ]:











  
    

      
      107
    

  
  
    

      id
      ../../data/extracted_images/ref/107.jpg
    

    

      x
      962.894876
    

    

      y
      610.847041
    

    

      r1
      8.444318
    

    

      r2
      8.67007
    

    

      theta
      56.957356
    

    

      r
      8.319342
    

    

      Region
      II
    

    

      time
      107
    

    

      vx
      4.736515
    

    

      vy
      -2.588445
    

    

      v
      5.39765
    

    

      angle
      28.656041
    

  



























In [ ]:



     


angle_at_contact_frame_s = df_s.loc[contact_frame_num]["angle"]
angle_at_leave_frame_s = df_s.loc[leave_frame_num]["angle"]

angle_at_contact_frame_c = df_c.loc[contact_frame_num]["angle"]
angle_at_leave_frame_c = df_c.loc[leave_frame_num]["angle"]


if angle_at_contact_frame_s < 0:
    angle_at_contact_frame_s = 180 + angle_at_contact_frame_s

if angle_at_contact_frame_c < 0:
    angle_at_contact_frame_c = 180 + angle_at_contact_frame_c


angle_at_contact_frame_c, angle_at_contact_frame_s, angle_at_leave_frame_c, angle_at_leave_frame_s



     






















    
    
Out[ ]:








(88.31531568210372, 89.298416994945, 30.068582821862446, 28.65604087866925)




























Speeds¶


















In [ ]:



     


velocity_at_leave_frame_s = df_s.loc[leave_frame_num]["v"]
velocity_at_contact_frame_s = df_s.loc[contact_frame_num]["v"]
velocity_at_leave_frame_s, velocity_at_contact_frame_s



     






















    
    
Out[ ]:








(5.397649793125025, 5.2786822041945936)
























In [ ]:



     


velocity_at_leave_frame_c = df_c.loc[leave_frame_num]["v"]
velocity_at_contact_frame_c = df_c.loc[contact_frame_num]["v"]
velocity_at_leave_frame_c, velocity_at_contact_frame_c



     






















    
    
Out[ ]:








(6.272713828600043, 4.859243243341414)
























In [ ]:



     


x_velocity_at_leave_frame_s = df_s.loc[leave_frame_num]["vx"]
x_velocity_at_contact_frame_s = df_s.loc[contact_frame_num]["vx"]
y_velocity_at_leave_frame_s = df_s.loc[leave_frame_num]["vy"]
y_velocity_at_contact_frame_s = df_s.loc[contact_frame_num]["vy"]
print(
    x_velocity_at_leave_frame_s,
    x_velocity_at_contact_frame_s,
    y_velocity_at_leave_frame_s,
    y_velocity_at_contact_frame_s,
)

x_velocity_at_leave_frame_c = df_c.loc[leave_frame_num]["vx"]
x_velocity_at_contact_frame_c = df_c.loc[contact_frame_num]["vx"]
y_velocity_at_leave_frame_c = df_c.loc[leave_frame_num]["vy"]
y_velocity_at_contact_frame_c = df_c.loc[contact_frame_num]["vy"]
print(
    x_velocity_at_leave_frame_c,
    x_velocity_at_contact_frame_c,
    y_velocity_at_leave_frame_c,
    y_velocity_at_contact_frame_c,
)



     






















    
    






4.736515139237748 -0.06463549685330301 -2.5884450206628378 5.27828647057236
5.428571428571429 -0.14285714285714285 -3.142857142857143 4.857142857142857




























Fitting Curves¶






















The Curves to be Fitted¶






















We'll assume that downward is the positive direction. In this way, the gravitational acceleration is positive. In x direction, no force is acting and hence the equation of motion is simply:

$$
x(t) = x_0 + v_{x0}t
$$
Here $x_0$ is the initial x position, $v_{x0}$ is the initial y velocity.























Now, in y direction, the equation of motion is:

$$
y(t) = y_0 + v_{y0}t + \frac{1}{2}gt^2
$$
Here, $y_0$ is the initial y position, $v_{y0}$ is the initial y velocity, and $g$ is the acceleration due to gravity.























We'll optimize these two equations to get the initial velocity and the initial position for x and y direction.























We can also phrase the same problem by eliminating $t$ from the equation of motions. This way, we'll get $y$ as a function of $x$. Eliminating $t$ from the equation of motion, we get:

$$
y = y_0 + \frac{v_y}{v_x}(x - x_0) + \frac{1}{2}g\frac{(x - x_0)^2}{v_x^2}
$$





















Here, we have rewritten $v_{x0}$ as $v_x$ and $v_{y0}$ as $v_y$.























This is a parabola with the parameters $x_0$, $y_0$, $v_y$, $v_x$ and $g$. We can use scipy to get these parameters. However, as we already know the values of $x_0$ and $y_0$ with reasonable accuracy, we'll use them.























Similarly, fitting the first two equations gives the same parameters.



















In [ ]:



     


def the_parabola_to_fit(x, m, a, x0, y0):
    second_term = (m) * (x - x0)
    third_term = a * ((x - x0) ** 2)
    return y0 + second_term + third_term


def parametric_x_to_fit(t, vx0, x0):
    return x0 + vx0 * t


def parametric_y_to_fit(t, vy0, g, y0):
    return y0 + vy0 * t + 0.5 * g * t**2



     























Region III¶






















Data For Region III¶


















In [ ]:



     


region_3 = df_c[df_c["Region"] == "III"]



     



















In [ ]:



     


X = region_3["x"].values
x0 = X[0]
Y = region_3["y"].values
y0 = Y[0]
t = region_3["time"].values
offset = t[0]
tbar = t - offset



     



















In [ ]:



     


x0, y0



     






















    
    
Out[ ]:








(969.0, 606.0)
























In [ ]:



     


tbar



     






















    
    
Out[ ]:








array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
       17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
       34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50,
       51, 52], dtype=int64)




























Fitting the Curves In Region III¶


















In [ ]:



     


the_parabola = partial(the_parabola_to_fit, x0=x0, y0=y0)
parametric_x = partial(parametric_x_to_fit, x0=x0)
parametric_y = partial(parametric_y_to_fit, y0=y0)
the_parabola_vector = np.vectorize(the_parabola)
parametric_x_vector = np.vectorize(parametric_x)
parametric_y_vector = np.vectorize(parametric_y)



     



















In [ ]:



     


popt, pcov = curve_fit(the_parabola, X, Y)
popty, pcovy = curve_fit(parametric_y, tbar, Y)
poptx, pcovx = curve_fit(parametric_x, tbar, X)



     



















In [ ]:



     


popt, popty, poptx



     






















    
    
Out[ ]:








(array([-0.52754421,  0.00195145]),
 array([-2.52394612,  0.08890582]),
 array([4.74636119]))




























Caparing Results For Region III¶






















Using

$$
m = \frac{v_y}{v_x}\\
a = \frac{g}{2v_x^2}
$$
we can check whether the parameters by both the equations are the same.



















In [ ]:



     


m_by_parametric = popty[0] / poptx[0]
m_by_parabola = popt[0]
m_by_parametric, m_by_parabola



     






















    
    
Out[ ]:








(-0.5317644437316823, -0.5275442095377482)
























In [ ]:



     


a_by_parametric = popty[1] / poptx[0] ** 2 / 2
a_by_parabola = popt[1]
a_by_parametric, a_by_parabola



     






















    
    
Out[ ]:








(0.0019732342128660173, 0.0019514472283770265)




























Calculating Informations From Parameters In Region III¶






















The Speeds In Region III¶






















Next, we'll see how the calculated velocities are? The eqaution for the speeds are:

$$
v_x(t) = v_{x0}\\
v_y(t) = v_{y0} + gt
$$

















In [ ]:



     


vy = popty[0] + popty[1] * (tbar)
vx = np.ones(len(tbar)) * poptx[0]
v = np.sqrt(vy**2 + vx**2)



     























The Angle In Region III¶






















Next, let's calculate the angle between the x and y velocity.



















In [ ]:



     


angles = np.arctan(vy / vx) * 180 / np.pi



     























Visualizating Results In Region III¶






















x and y Coordinates In Region III¶


















In [ ]:



     


plt.scatter(tbar, X, label="X Data")
title = "X vs Time for Region III"
plt.plot(tbar, parametric_x_vector(tbar, *poptx), "r", label="X Fitted")
plt.legend()
plt.xlabel("Time in ms")
plt.ylabel("X in pixels")
plt.title(title)
save_name = RESULT_DIR + "/" + title.replace(" ", "_") + ".png"
plt.savefig(save_name)
plt.show()



     






















    
    































In [ ]:



     


plt.scatter(tbar, Y, label="y Data")
title = "Y vs Time for Region III"
plt.plot(tbar, parametric_y_vector(tbar, *popty), "r", label="y Fitted")
plt.legend()
plt.xlabel("Time in ms")
plt.ylabel("y in pixels")
plt.title(title)
save_name = RESULT_DIR + "/" + title.replace(" ", "_") + ".png"
plt.savefig(save_name)
plt.show()



     






















    
    































In [ ]:



     


plt.plot(X, Y, "o", label="x vs y Data")
title = "X vs Y for Region III Using Parabola"
plt.plot(X, the_parabola_vector(X, *popt), "r", label="x vs y with Parabola")
plt.legend()
plt.xlabel("x in pixels")
plt.ylabel("y in pixels")
plt.title(title)
save_name = RESULT_DIR + "/" + title.replace(" ", "_") + ".png"
plt.savefig(save_name)
plt.show()



     






















    
    































In [ ]:



     


plt.plot(X, Y, "o", label="x vs y Data")
title = "X vs Y for Region III Using Parametric"
plt.plot(parametric_x_vector(tbar, *poptx), parametric_y_vector(tbar, *popty), "r", label="x vs y with Parametric")
plt.legend()
plt.xlabel("x in pixels")
plt.ylabel("y in pixels")
plt.title(title)
save_name = RESULT_DIR + "/" + title.replace(" ", "_") + ".png"
plt.savefig(save_name)
plt.show()



     






















    
    



































Speeds In Region III¶


















In [ ]:



     


plt.plot(tbar, region_3["vx"].values, label="$v_x$ Data")
title = "$v_x$ vs Time for Region III"
plt.plot(tbar, vx, "r", label="$v_x$ Calculated")
plt.legend()
plt.xlabel("Time in ms")
plt.ylabel("$v_x$ in pixels/ms")
plt.title(title)
save_name = RESULT_DIR + "/" + title.replace(" ", "_").replace("$", "") + ".png"
plt.savefig(save_name)
plt.show()



     






















    
    































In [ ]:



     


plt.plot(tbar, region_3["vy"].values, label="$v_y$ Data")
title = "$v_y$ vs Time for Region III"
plt.plot(tbar, vy, "r", label="$v_y$ Calculated")
plt.legend()
plt.xlabel("Time in ms")
plt.ylabel("$v_y$ in pixels/ms")
plt.title(title)
save_name = RESULT_DIR + "/" + title.replace(" ", "_").replace("$", "") + ".png"
plt.savefig(save_name)
plt.show()



     






















    
    































In [ ]:



     


plt.plot(tbar, region_3["v"].values, label="$v$ Data")
title = "$v$ vs Time for Region III"
plt.plot(tbar, v, "r", label="$v$ Calculated")
plt.legend()
plt.xlabel("Time in ms")
plt.ylabel("$v$ in pixels/ms")
plt.title(title)
save_name = RESULT_DIR + "/" + title.replace(" ", "_").replace("$", "") + ".png"
plt.savefig(save_name)
plt.show()



     






















    
    



































Angle In Region III¶


















In [ ]:



     


plt.plot(region_3["angle"].values, label="Angle data")
title = "Angle vs Time for Region III"
plt.plot(-angles, "r", label="Angle calculated")
plt.xlabel("Time in ms")
plt.ylabel("Angle in degrees")
plt.title(title)
save_name = RESULT_DIR + "/" + title.replace(" ", "_") + ".png"
plt.savefig(save_name)
plt.legend()
plt.show()



     






















    
    



































Getting The Required Informations In Region III¶


















In [ ]:



     


g_raw = popty[1]
vx_using_curve = poptx[0]
vy_using_curve = popty[1]
v_using_curve = np.sqrt(vx_using_curve**2 + vy_using_curve**2)



     



















In [ ]:



     


fps = 1000
pixels = 0.0115
speed_conversion = pixels * fps
acceleration_conversion = pixels * fps**2
g_in_region_3 = g_raw * acceleration_conversion
g_in_region_3



     






















    
    
Out[ ]:








1022.4169495159215
























In [ ]:



     


x_velocity_at_leave_frame_using_c = vx[0]
y_velocity_at_leave_frame_using_c = vy[0]
velocity_at_leave_frame_using_c = v[0]
angle_at_leave_frame_using_c = angles[0]
x_velocity_at_leave_frame_using_c, y_velocity_at_leave_frame_using_c, velocity_at_leave_frame_using_c, angle_at_leave_frame_using_c



     






















    
    
Out[ ]:








(4.746361185991997,
 -2.5239461158186822,
 5.375709116335032,
 -28.002457200364926)




























Adding the Information for Region III to DataFrame¶


















In [ ]:



     


new_info_df_for_region_3 = pd.DataFrame(
    {"vx": vx, "vy": vy, "v": v, "angle": angles, "time": t}
)
new_info_df_for_region_3.columns = [
    "vx_using_curve",
    "vy_using_curve",
    "v_using_curve",
    "angle_using_curve",
    "time",
]



     























Region I¶






















Data For Region I¶


















In [ ]:



     


region_1 = df_c[df_c["Region"] == "I"]



     



















In [ ]:



     


X = region_1["x"].values
x0 = X[0]
Y = region_1["y"].values
y0 = Y[0]
t = region_1["time"].values
offset = t[0]
tbar = t - offset



     



















In [ ]:



     


x0, y0



     






















    
    
Out[ ]:








(870.0, 411.0)
























In [ ]:



     


tbar



     






















    
    
Out[ ]:








array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
       17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
       34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50])




























Fitting the Curves¶


















In [ ]:



     


the_parabola = partial(the_parabola_to_fit, x0=x0, y0=y0)
parametric_x = partial(parametric_x_to_fit, x0=x0)
parametric_y = partial(parametric_y_to_fit, y0=y0)
the_parabola_vector = np.vectorize(the_parabola)
parametric_x_vector = np.vectorize(parametric_x)
parametric_y_vector = np.vectorize(parametric_y)



     



















In [ ]:



     


popt, pcov = curve_fit(the_parabola, X, Y)
popty, pcovy = curve_fit(parametric_y, tbar, Y)
poptx, pcovx = curve_fit(parametric_x, tbar, X)



     



















In [ ]:



     


popt, popty, poptx



     






















    
    
Out[ ]:








(array([-32.63023863,   1.64840318]),
 array([1.05835668, 0.08616752]),
 array([-0.06867793]))




























Caparing Results¶






















Using

$$
m = \frac{v_y}{v_x}\\
a = \frac{g}{2v_x^2}
$$
we can check whether the parameters by both the equations are the same.



















In [ ]:



     


m_by_parametric = popty[0] / poptx[0]
m_by_parabola = popt[0]
m_by_parametric, m_by_parabola



     






















    
    
Out[ ]:








(-15.410434368564319, -32.630238632389656)
























In [ ]:



     


a_by_parametric = popty[1] / poptx[0] ** 2 / 2
a_by_parabola = popt[1]
a_by_parametric, a_by_parabola



     






















    
    
Out[ ]:








(9.134383905042618, 1.6484031817656235)




























Calculating Informations From Parameters¶






















The Speeds¶






















Next, we'll see how the calculated velocities are? The eqaution for the speeds are:

$$
v_x(t) = v_{x0}\\
v_y(t) = v_{y0} + gt
$$

















In [ ]:



     


vy = popty[0] + popty[1] * (tbar)
vx = np.ones(len(tbar)) * poptx[0]
v = np.sqrt(vy**2 + vx**2)



     























The Angle¶






















Next, let's calculate the angle between the x and y velocity.



















In [ ]:



     


angles = np.arctan(vy / vx) * 180 / np.pi



     























Visualizating Results¶






















x and y Coordinates¶


















In [ ]:



     


plt.scatter(tbar, X, label="X Data")
title = "X vs Time for Region I"
plt.plot(tbar, parametric_x_vector(tbar, *poptx), "r", label="X Fitted")
plt.legend()
plt.xlabel("Time in ms")
plt.ylabel("X in pixels")
plt.title(title)
save_name = RESULT_DIR + "/" + title.replace(" ", "_") + ".png"
plt.savefig(save_name)
plt.show()



     






















    
    































In [ ]:



     


plt.scatter(tbar, Y, label="y Data")
title = "Y vs Time for Region I"
plt.plot(tbar, parametric_y_vector(tbar, *popty), "r", label="y Fitted")
plt.legend()
plt.xlabel("Time in ms")
plt.ylabel("y in pixels")
plt.title(title)
save_name = RESULT_DIR + "/" + title.replace(" ", "_") + ".png"
plt.savefig(save_name)
plt.show()



     






















    
    































In [ ]:



     


plt.plot(X, Y, "o", label="x vs y Data")
title = "X vs Y for Region I Using Parabola"
plt.plot(X, the_parabola_vector(X, *popt), "r", label="x vs y with Parabola")
plt.legend()
plt.xlabel("x in pixels")
plt.ylabel("y in pixels")
plt.title(title)
save_name = RESULT_DIR + "/" + title.replace(" ", "_") + ".png"
plt.savefig(save_name)
plt.show()



     






















    
    































In [ ]:



     


plt.plot(X, Y, "o", label="x vs y Data")
title = "X vs Y for Region I Using Parametric"
plt.plot(parametric_x_vector(tbar, *poptx), parametric_y_vector(tbar, *popty), "r", label="x vs y with Parametric")
plt.legend()
plt.xlabel("x in pixels")
plt.ylabel("y in pixels")
plt.title(title)
save_name = RESULT_DIR + "/" + title.replace(" ", "_") + ".png"
plt.savefig(save_name)
plt.show()



     






















    
    



































Speeds¶


















In [ ]:



     


plt.plot(tbar, region_1["vx"].values, label="$v_x$ Data")
title = "$v_x$ vs Time for Region I"
plt.plot(tbar, vx, "r", label="$v_x$ Calculated")
plt.legend()
plt.xlabel("Time in ms")
plt.ylabel("$v_x$ in pixels/ms")
plt.title(title)
save_name = RESULT_DIR + "/" + title.replace(" ", "_").replace("$", "") + ".png"
plt.savefig(save_name)
plt.show()



     






















    
    































In [ ]:



     


plt.plot(tbar, region_1["vy"].values, label="$v_y$ Data")
title = "$v_y$ vs Time for Region I"
plt.plot(tbar, vy, "r", label="$v_y$ Calculated")
plt.legend()
plt.xlabel("Time in ms")
plt.ylabel("$v_y$ in pixels/ms")
plt.title(title)
save_name = RESULT_DIR + "/" + title.replace(" ", "_").replace("$", "") + ".png"
plt.savefig(save_name)
plt.show()



     






















    
    































In [ ]:



     


plt.plot(tbar, region_1["v"].values, label="$v$ Data")
title = "$v$ vs Time for Region I"
plt.plot(tbar, v, "r", label="$v$ Calculated")
plt.legend()
plt.xlabel("Time in ms")
plt.ylabel("$v$ in pixels/ms")
plt.title(title)
save_name = RESULT_DIR + "/" + title.replace(" ", "_").replace("$", "") + ".png"
plt.savefig(save_name)
plt.show()



     






















    
    



































Angle¶


















In [ ]:



     


plt.plot(region_1["angle"].values, label="Angle data")
title = "Angle vs Time for Region I"
plt.plot(-angles, "r", label="Angle calculated")
plt.xlabel("Time in ms")
plt.ylabel("Angle in degrees")
plt.title(title)
save_name = RESULT_DIR + "/" + title.replace(" ", "_") + ".png"
plt.savefig(save_name)
plt.legend()
plt.show()



     






















    
    



































Getting The Required Informations¶


















In [ ]:



     


fps = 1000
pixels = 0.0115
speed_conversion = pixels * fps
acceleration_conversion = pixels * fps**2
g_raw = popty[1]
g_in_region_1 = g_raw * acceleration_conversion
g_in_region_1



     






















    
    
Out[ ]:








990.9265101122728
























In [ ]:



     


x_velocity_at_contact_frame_using_c = vx[-1]
y_velocity_at_contact_frame_using_c = vy[-1]
velocity_at_contact_frame_using_c = v[-1]
angle_at_contact_frame_using_c = angles[-1]
x_velocity_at_contact_frame_using_c, y_velocity_at_contact_frame_using_c, velocity_at_contact_frame_using_c, angle_at_contact_frame_using_c



     






















    
    
Out[ ]:








(-0.06867792661852179,
 5.366732811646731,
 5.3671722283908725,
 -89.2668275651495)
























In [ ]:



     


h_using_c = Y[-1] - Y[0]
h_using_c



     






















    
    
Out[ ]:








160.0
























In [ ]:



     


if angle_at_contact_frame_using_c < 0:
    angle_at_contact_frame_using_c = angle_at_contact_frame_using_c + 180



     



















In [ ]:



     


new_info_df_for_region_1 = pd.DataFrame(
    {"vx": vx, "vy": vy, "v": v, "angle": angles, "time": t}
)
new_info_df_for_region_1.columns = [
    "vx_using_curve",
    "vy_using_curve",
    "v_using_curve",
    "angle_using_curve",
    "time",
]



     























Adding the Additional Information¶






















Saving Informations to DataFrame¶


















In [ ]:



     


info_df = pd.concat([new_info_df_for_region_1, new_info_df_for_region_3], axis=0)



     



















In [ ]:



     


df_final = pd.merge(df_c, info_df, on="time", how="left")
df_final.head()



     






















    
    
Out[ ]:











  
    

      
      id
      x
      y
      r1
      r2
      theta
      Region
      time
      vx
      vy
      v
      angle
      vx_using_curve
      vy_using_curve
      v_using_curve
      angle_using_curve
    

  
  
    

      0
      ../../data/extracted_images/ref/007.jpg
      870.0
      404.0
      11.0
      10.0
      100.267614
      O
      7
      0.142857
      0.142857
      0.202031
      -45.000000
      NaN
      NaN
      NaN
      NaN
    

    

      1
      ../../data/extracted_images/ref/008.jpg
      870.0
      405.0
      11.0
      10.0
      87.662543
      O
      8
      0.142857
      0.285714
      0.319438
      -63.434949
      NaN
      NaN
      NaN
      NaN
    

    

      2
      ../../data/extracted_images/ref/009.jpg
      870.0
      405.0
      11.0
      10.0
      76.203387
      O
      9
      0.142857
      0.285714
      0.319438
      -63.434949
      NaN
      NaN
      NaN
      NaN
    

    

      3
      ../../data/extracted_images/ref/010.jpg
      871.0
      406.0
      10.0
      11.0
      128.915504
      O
      10
      0.285714
      0.428571
      0.515079
      -56.309932
      NaN
      NaN
      NaN
      NaN
    

    

      4
      ../../data/extracted_images/ref/011.jpg
      870.0
      406.0
      11.0
      10.0
      29.793805
      O
      11
      0.142857
      0.428571
      0.451754
      -71.565051
      NaN
      NaN
      NaN
      NaN
    

  































The Text Information¶






















Creating the Text¶


















In [ ]:



     


pattern = "***"
information = f"""
{pattern*20}
### TOTAL FRAMES: {total_frames}
### NONE FRAMES: {none_frames}
### UNREALISTIC FRAMES: {unrealistic}
### PASSTHROUGH: {passthrough}

{pattern*20}
USING THE SMOOTHENED DATA
AT CONTACT FRAME:
### H: {np.round(hs, 1)}
### ANGLE: {np.round(-90+angle_at_contact_frame_s+float(angle), 2)}
### VELOCITY: {np.round(velocity_at_contact_frame_s, 2)}
### X VELOCITY: {np.round(x_velocity_at_contact_frame_s, 2)}
### Y VELOCITY: {np.round(y_velocity_at_contact_frame_s, 2)}

AT LEAVE FRAME:
### ANGLE: {np.round(angle_at_leave_frame_s, 2)}
### VELOCITY: {np.round(velocity_at_leave_frame_s, 2)}
### X VELOCITY: {np.round(x_velocity_at_leave_frame_s, 2)}
### Y VELOCITY: {np.round(y_velocity_at_leave_frame_s, 2)}

{pattern*20}
USING THE RAW DATA
AT CONTACT FRAME:
### H: {np.round(hc, 1)}
### ANGLE: {np.round(-90+angle_at_contact_frame_c+float(angle), 2)}
### VELOCITY: {np.round(velocity_at_contact_frame_c, 2)}
### X VELOCITY: {np.round(x_velocity_at_contact_frame_c, 2)}
### Y VELOCITY: {np.round(y_velocity_at_contact_frame_c, 2)}

AT LEAVE FRAME:
### ANGLE: {np.round(angle_at_leave_frame_c, 2)}
### VELOCITY: {np.round(velocity_at_leave_frame_c, 2)}
### X VELOCITY: {np.round(x_velocity_at_leave_frame_c, 2)}
### Y VELOCITY: {np.round(y_velocity_at_leave_frame_c, 2)}

{pattern*20}
USING CURVE FITTING
AT CONTACT FRAME:
### H: {np.round(h_using_c, 1)}
### ANGLE: {np.round(-90+angle_at_contact_frame_using_c+float(angle), 2)}
### VELOCITY: {np.round(velocity_at_contact_frame_using_c, 2)}
### X VELOCITY: {np.round(x_velocity_at_contact_frame_using_c, 2)}
### Y VELOCITY: {np.round(y_velocity_at_contact_frame_using_c, 2)}
### g: {np.round(g_in_region_1, 2)}

AT LEAVE FRAME:
### ANGLE: {np.round(-angle_at_leave_frame_using_c, 2)}
### VELOCITY: {np.round(velocity_at_leave_frame_using_c, 2)}
### X VELOCITY: {np.round(x_velocity_at_leave_frame_using_c, 2)}
### Y VELOCITY: {np.round(y_velocity_at_leave_frame_using_c, 2)}
### g: {np.round(g_in_region_3, 2)}
"""
print(information)



     






















    
    






************************************************************
### TOTAL FRAMES: 171
### NONE FRAMES: 3
### UNREALISTIC FRAMES: 3
### PASSTHROUGH: 0

************************************************************
USING THE SMOOTHENED DATA
AT CONTACT FRAME:
### H: 164.3
### ANGLE: 23.8
### VELOCITY: 5.28
### X VELOCITY: -0.06
### Y VELOCITY: 5.28

AT LEAVE FRAME:
### ANGLE: 28.66
### VELOCITY: 5.4
### X VELOCITY: 4.74
### Y VELOCITY: -2.59

************************************************************
USING THE RAW DATA
AT CONTACT FRAME:
### H: 161.0
### ANGLE: 22.82
### VELOCITY: 4.86
### X VELOCITY: -0.14
### Y VELOCITY: 4.86

AT LEAVE FRAME:
### ANGLE: 30.07
### VELOCITY: 6.27
### X VELOCITY: 5.43
### Y VELOCITY: -3.14

************************************************************
USING CURVE FITTING
AT CONTACT FRAME:
### H: 160.0
### ANGLE: 25.23
### VELOCITY: 5.37
### X VELOCITY: -0.07
### Y VELOCITY: 5.37
### g: 990.93

AT LEAVE FRAME:
### ANGLE: 28.0
### VELOCITY: 5.38
### X VELOCITY: 4.75
### Y VELOCITY: -2.52
### g: 1022.42





























First, create a new string containing just the previous text file. Else we'll duplicate the text file.



















In [ ]:



     


with open(RESULT_DIR + "/info.txt", "r+") as f:
    texts = f.readlines()
    text = "".join(texts[:6])
print(text[:125])
all_text = text + information



     






















    
    






### ref.tif
### First Frame ID: 017
### Last Frame ID: 161
### Contact Frame ID: 068
### Leave Frame ID: 107
### Angle: 24.5

























In [ ]:



     


with open(RESULT_DIR + "/info.txt", "w") as f:
    f.writelines(all_text)



     























Save the DataFrames¶


















In [ ]:



     


df_final.to_csv(RESULT_DIR + f"/{sequence}_final.csv", index=False)
df_s.to_csv(RESULT_DIR + f"/{sequence}_smoothened.csv", index=False)
df_c.to_csv(RESULT_DIR + f"/{sequence}_raw.csv", index=False)